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Question

Find the distance of the point of intersection of the lines 2x+3y=21 and 3x4y+11=0 from the line 8x+6y+5=0

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Solution

since the equation of lines which been intersected is given as;

2x+3y=21(1)

and 3x4y+11=03x4y=11(2)

(1)×4+(2)×3

8x+12y=84
9x12y=33
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯17x+0=51

x=34y=20 y=5

x=3 and y=5

coordinate of point of intersection is (3,5)

since the distance of point (3,5) from the line 8x+6y+5=0 is given as

d=|Ax1+By1+C|A2+B2

=|83+65+5|82+62

=5910

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